question is: What if I attack/block with Slaves in Egypt and capture them to opponent's LoB? Do they count as both Hero and EC there or do they only count as the alignment with which they have been played (I'd say the latter case applies)?

Slaves in Egypt:You may capture this character to opponent's Land of Bondage to take an Exodus Fortress from deck or Reserve and add an Exodus character to battle.

Per the REG, captured characters are treated as neutral, unless an ability specifies targeting of what kind of character is captured, such as Covenant of Palestine (PoC). So if Slaves was captured to your opponent’s LoB as a hero, if a EC tried to negate a good card, your opponent could not target Slaves because it’s no longer aligned to good but to neutral.

Per the REG, captured characters are treated as neutral, unless an ability specifies targeting of what kind of character is captured, such as Covenant of Palestine (PoC). So if Slaves was captured to your opponent’s LoB as a hero, if a EC tried to negate a good card, your opponent could not target Slaves because it’s no longer aligned to good but to neutral.

Thank you. And what does this mean if I try to use Lamb's Righteousness on Slaves? Do they always count as Hero then, regardless whether I captured them used as blocker?

Lamb's Righteousness:If rescuing and your Hero is opposed, you may rescue a captured Hero in opponent's territory. If you do, restrict yourself from rescuing additional cards this turn.

Per the REG, captured characters are treated as neutral, unless an ability specifies targeting of what kind of character is captured, such as Covenant of Palestine (PoC). So if Slaves was captured to your opponent’s LoB as a hero, if a EC tried to negate a good card, your opponent could not target Slaves because it’s no longer aligned to good but to neutral.

Thank you. And what does this mean if I try to use Lamb's Righteousness on Slaves? Do they always count as Hero then, regardless whether I captured them used as blocker?

Lamb's Righteousness:If rescuing and your Hero is opposed, you may rescue a captured Hero in opponent's territory. If you do, restrict yourself from rescuing additional cards this turn.

*I think* the takeaway here is that you can think of them as a captured "whatever they were when they were captured" with neutral alignment.